easy to remember greeks in deriv. just look at the first letter Theta - Related to "T"ime Vega - Related to "V"olatility Rho - "R"isk free rate Delta - Well this one doesnt work as well, A for asset price Stupid yes, but helps me to remember! Just under 4 weeks to go…
^ not stupid. that is how it is mentioned in the text, and if it works, why not? 
There are five input to BSM. Of these input, eXercise price is not involved with the Greeks (remember the big “X”). So for the remaining ones, just remember it like how you described. The last one (Delta) would be matched with the last variable (asset price) by process of elimination.
forgetting gamma. But the point your missing , is what these underlying greeks mean in evaluating options. i.e. what effect thats vega have on a put and call; when is your delta largest; etc. good thing I am a trader, so can skip this topic